Numerical Assessment of the Boundary Layer Effect Predicted by the Shear Flexible Beam Theory with the Sixth-order Differential Equations

摘要

The analytical solutions of shear flexible beams with displacement boundary conditions are derived by using the new sixth-order differential equation beam theory presented by Shi and Voyiadjis (ASME J. Appl. Mech., Vol. 78, 021019, 2011), in which the boundary layer effects are included. The accuracy of the boundary layer effects predicted by the new sixth-order beam theory is evaluated by the finite element analysis in this study. The numerical results show that the new sixth-order beam theory is capable of taking account of the displacement boundary conditions of shear deformable beams and predicting good results of the boundary layer effects induced by the displacement boundaries and the continuity constraints.